Quantum Physics

Title:
PEPS as ground states: degeneracy and topology

Abstract: We introduce a framework for characterizing Matrix Product States (MPS) and
Projected Entangled Pair States (PEPS) in terms of symmetries. This allows us
to understand how PEPS appear as ground states of local Hamiltonians with
finitely degenerate ground states and to characterize the ground state
subspace. Subsequently, we apply our framework to show how the topological
properties of these ground states can be explained solely from the symmetry: We
prove that ground states are locally indistinguishable and can be transformed
into each other by acting on a restricted region, we explain the origin of the
topological entropy, and we discuss how to renormalize these states based on
their symmetries. Finally, we show how the anyonic character of excitations can
be understood as a consequence of the underlying symmetries.